Ask A Scientist Chemistry Archive

name         Jason G.
status       educator
age          20s

Question -   One of my students is 'hounding' me for an answer to this question:  How many water 
molecules are contained within an 8-ounce glass of water?
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Jason,

Let us for sake of convenience assume the eight ounces of water is its weight rather than 
volume -- they are both close. An ounce is about 28 grams.

(8 ounces of water)(28 grams per ounce) = 224 grams of water.

16 grams of water represents one "mole" of water -- a mole of anything contains 6.02x10^23 
particles -- in this particular case, molecules. By the way, that number is referred to as 
the Avogadro number -- named after the pioneering Italian scientist who determined its value. 
It is very large, and in a way, it is a testament to how small molecules really are.

(224 grams of water) divided by (18 grams per mole) = 12.4 moles

(12.4 moles of water)(6.02x10^23) molecules per mole = 7.5x10^24 molecules in the 8 ounce 
glass of water.

As you can see, the answer to the student's question results in an unimaginably large number. 
To put it in a little perspective, humans will never makes a device that can lift 6.02X10^23 
of anything you could see even with a powerful microscope. Fact or fancy?

Let us for fun assume that a germ weighed a billionth of a gram -- that is 1x10^-9 grams, a 
very small weight.

Now let us say we have an Avogadro number of "germs."

(1x10^-9 grams per "germ")(6.02x10^23 "germs") = 6.02x10^14 grams for the collection

(6.02x10^14 grams) divided by (454 grams per pound) = 1.33x10^12 pounds

(1.33x10^12 pounds) divided by (2000 pounds per ton) = 662,995,594 tons.

No, humans will not ever have a machine that will be able to lift an Avogadro number of things 
that weigh even a billionth of a gram. Even so, we can easily lift and drink the 7.5x10^24 
molecules in the 8 ounce glass of water. Water molecules are pretty small

Regards,
ProfHoff 753
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Here are the necessary conversions: 1 oz. = 29.57 cm^3, so 8 oz. = 236.6 cm^3. The density of 
water is
1cm^3 water = 1gm water, so 236.6 cm^3 water = 236.6 gm water. The molecular
weight of water is 18 gm/mol, so 236.6 gm water = 236.6 / 18 mols water = 13.14 mols water. 
One mole of anything is equal to
6.02x10^23 things. So 13.14 mols of water = 13.14 x 6.02x10^23 molecules = 7.9x10^24 molecules. 
That is a big number!

Vince Calder
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Hi,

The density of water is about 1 gram per mL. Water weighs about 18 grams per mole. A mole has 
about 6.0 x 10^23 molecules.
There are about 30 mL per fluid ounce. There are 8 ounces of water.

SO....using dimensional analysis...

number of molecules = (1 gram/mL)*(1 mole/18 grams)*(6.0x10^23 molecules/mole)*(30 mL/ounce)*8 
ounces

= 8 X 10^24 molecules!

A LOT.

Best, prof. topper
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1 liter of water has mass about 1000 grams/liter.  Water has molecular weight about 18 
grams/mole (2 hydrogens = 2, 1 oxygen = 16).  So that is 1000/18 = 55 moles/liter.  A 
mole is 6 x 10 to the 23 power (6.023x10^23) molecules.  So in 1 liter there are 55 times 
that, number of molecules.  There are about 4 8-oz cups in a liter (you can be more accurate 
but why?)  So divide by 4.

6.x10^23 * 55 / 4 = about 10^25, 1 followed by 25 zeroes, number of  water molecules.  Give 
or take.

Steve Ross
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Jason G.,

Given the following information:

1. One 8 ounce glass of water.
2. One cubic centimeter equals one milliliter.
3. A one ounce glass of water equals 29.57 milliliters.
4. One mole of water is 18.0 grams.
5. One mole is equal to 6.02 times 10 to the 23rd power.
6. The density of water is 1.0 grams per milliliter at room temperature.

A 8 ounce glass of water at room temperature has 7.91 times ten to the 24th
power molecules.

Sincerely,

Bob Trach
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